## Featured resource

### Defining Mathematics Education *REDUCED*

The Seventy-fifth Yearbook is a celebration and reflection of the history of the NCTM yearbooks, and is a great resource on the key issues of mathematics education through the years.

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# Big ideas

Mental computation is the ability to work out the answer to a calculation mentally. It requires the recall of number facts and the use of a range of thinking strategies.

There are four big ideas that underpin mental computation.

• Knowledge influences the range of possible strategies. It enables students to choose appropriate strategies. The range of key knowledge is broader than the essential basic facts for addition, subtraction, multiplication and division. Key knowledge includes:
• place value
• number sequences
• understanding the meaning of symbols
• number properties.
• Searching for patterns and relationships helps students to make connections between mathematical ideas and within different contexts. Exploring patterns and relationships leads to generalisation of the properties of the four operations (e.g. using arrays to generalise the commutative property of multiplication).
• Fluency with mental computation is the ease with which a student carries out a calculation.
Flexibility is recognising the demands of a problem and choosing the best strategy for the numbers.
• Strategic thinking in mental computation is deciding which operation to use and then the best way to carry out that operation.

For further exploration of these ideas, you can read the articles Strategies For Going Mental and Is Your Classroom Mental? on the AAMT website.

## Key knowledge

Mental computation is dependent on knowledge of associations, knowledge of processes and knowledge of the connections between them.

## Generalising patterns and relationships

Making connections makes the learning of facts by association easier.

## Fluency and flexibility

Fluency is one of the four proficiency strands of the Australian Curriculum: Mathematics. Students who are fluent can choose flexibly and appropriately from the procedures they have available and carry out the procedures efficiently and accurately.

## Strategic choice

Mental computation requires students to make decisions about which operation to use and the best way to carry out the operation.